22 problems

Quaplectic classification conjecture. There are various physically different classes of minimal uncertainty states, parametrised by the geometry of this homogeneous space. The conj…

Equipartition duality. Among all such states, the phase-equipartitioned product state, unique when it exists, simultaneously (i) maximizes the entropy, (ii) minimizes every within-…

Kovrizhkin's conjecture. The Logvinenko–Sereda theorem holds for this lacunary set $F^c$.

Let $c3_{risk}$ and $c3_{returns}$ denote the standard deviations of portfolio risk and returns, respectively, as defined in modern portfolio theory. Let $b6$ be a lower bound infl…

Let a quantum system decohere in the basis of an observable ${\hat X}$. Variance reduction conjecture. The variance of ${\hat X}$ should decrease on average during the decoherence…

Wigderson's conjecture. The image of $\mathcal{F}_{p,2}^{(1)}$ is all of $\mathbb{R}_{>0}$.

Let $A_{+}(28)$ denote the optimal constant in the uncertainty principle of Bourgain, Clozel, and Kahane in dimension $28$. An optimal function is a function attaining this optimal…

Let $\Lambda\subset\mathbb{R}^2$ be the set considered in the paper, let $\psi_0$ be the distinguished map introduced earlier, and let…

Let $g\in L^2(\mathbb{R}^d)$, and let $\mathcal{R},\mathcal{L}\subset\mathbb{R}^d$ be measurable sets of finite measure. Define … where $\alpha(S)$ is the mean width … with $dv_d$…

In the thermodynamic description, variables occur in conjugate pairs, such as pressure and volume; the source does not specify additional notation or a precise mathematical formula…

Canonical quantum-limit conjecture. The expression above should be valid in general, including for uncharged particles, because the alternative expression for $\Delta x$ breaks dow…

Generalized Fourier kernel boundedness conjecture. Inequality $|B_{k,a}(x,y)|\le 1$ holds whenever

Hardy–polar duality conjecture. Under these assumptions, $(X,P)$ is an $\hbar$-polar quantum pair.

Judge's conjecture. The uncertainties satisfy

Standard-deviation requirement. The explicit presence of the standard deviation in some way, such as $\sigma(M^{out})$ or the inaccuracy $\bar{\epsilon}(A)$, is essential for formu…

The discussion concerns the comparison between quantum and classical chaos, understood as temporal complexity, and the Heisenberg uncertainty relation, which limits simultaneous kn…

Logical uncertainty-relations conjecture. This feature should lead to a logical formulation of the uncertainty relations.

Let $d\geq 1$ be an integer, let $S,\Sigma\subset\mathbb{R}^d$ be sets of finite measure, and let $\varphi\in L^2(\mathbb{R}^d)$. Denote by $\widehat{\varphi}$ the Fourier transfor…

Let $d\geq 1$ be an integer, let $\Sigma\subset\mathbb{R}^d$ be a set of finite positive measure, and let $\Sigma^*$ denote the centered ball with $|\Sigma^*|=|\Sigma|$. For…

Mustard's conjecture. In the case of $R^2$, Mustard conjectured that

Equality characterization conjecture. Equality in the N-volume inequality holds if and only if $A_1{}_0,\ldots,A_N{}_0$ are linearly dependent.

The N-volume inequality conjecture. For every $N\in{\mathbb N}$,